Regardless of how you found that thread, it hilariously parallels what's going on here--it's eerie, actually! The season before the one in question (2006), Stoops had guided his team to a 6-6 record and a bowl game. Forward to 2007. Stoops, who was in his 4th year as head coach at Arizona (his first head coaching gig, btw), had just lost a close game at home to a dismal New Mexico team. Additionally, he was pretty much directly responsible for the loss as he picked up a key 15 yard unsportsmanlike conduct penalty which allowed New Mexico to punch in the decisive TD. I'd guess that the thread you linked to pretty much sums up the feelings of Arizona fans at the time. FIRE STOOPS!!!1!1!
BTW, Arizona went on to beat #2 Oregon later that year, and Stoops has followed it up with a couple 8 win seasons. He's 2-0 this year (his 7th at Arizona), and I doubt many are calling for his head.